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Probability when throwing five six-sided dice

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Please help with the following problem.

Compute the probabilities for each of the following when you throw five six-handed dice.

1) What is the probability that all five have different numbers?

2) What is the probability that at least four are the same?

3) What is the probability that exactly three are sixes?

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(1) (6*5*4*3*2)/6^5 =.09259 or 5/54

(2) Probability that five are the same is 6/6^5 =.000771604 and the probability that four are the same is (6*5*5)/6^5 =.01929. So the probability of getting at least four the same is the sum of these two which is .0201
To find the probability that there are at least four, we have to add the probability that there are four plus the ...

Solution Summary

This solution helps compute the probabilities of various outcomes the throw of five six-handed dice. These situations include: all give having different numbers, at least four being the same, and all three being sixes. Calculations are provided along with detailed explanations.